1.3 Simplify completely 1.3.1 \( x-3-\frac{5 x-6}{2-x}-\frac{4}{x-2} \)

To simplify the expression \( x - 3 - \frac{5x - 6}{2 - x} - \frac{4}{x - 2} \), let's first recognize that \( 2 - x \) can be rewritten as \(-(x - 2)\). Therefore, we can rewrite the first fraction as: \[ \frac{5x - 6}{2 - x} = -\frac{5x - 6}{x - 2} \] Now, we can rewrite the expression: \[ x - 3 + \frac{5x - 6}{x - 2} - \frac{4}{x - 2} \] Combining the fractions: \[ x - 3 + \frac{(5x - 6) - 4}{x - 2} = x - 3 + \frac{5x - 10}{x - 2} = x - 3 + 5 \] Now simplify: \[ x + 2 - 3 = x - 1 \] So, the completely simplified expression is: \[ \boxed{x - 1} \]